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0095-1137/11/$12.00 doi:10.1128/JCM.02135-10

Copyright © 2011, American Society for Microbiology. All Rights Reserved.

Identification of Mycobacteria in Solid-Culture Media by Matrix-Assisted

Laser Desorption Ionization–Time of Flight Mass Spectrometry

Paul G. Saleeb,

1

Steven K. Drake,

2

Patrick R. Murray,

3

and Adrian M. Zelazny

3

*

Laboratory of Clinical Infectious Diseases, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland1; Critical Care Medicine Department, Clinical Center, National Institutes of Health, Bethesda, Maryland2; and

Microbiology Service, Department of Laboratory Medicine, Clinical Center, National Institutes of Health, Bethesda, Maryland3

Received 21 October 2010/Returned for modification 27 November 2010/Accepted 3 March 2011

Matrix-assisted laser desorption ionization–time of flight mass spectrometry (MALDI-TOF MS) has re-cently been introduced into the clinical microbiology laboratory as a rapid and accurate method to identify bacteria and yeasts. In this paper we describe our work on the use of MALDI-TOF MS for the identification of mycobacterial isolates. We developed a protocol for protein extraction from mycobacteria and utilized it to construct a database containing 42 clinically relevant type and reference strains of mycobacteria. The database

was used to identify 104 clinical isolates of mycobacteria. All members of the Mycobacterium tuberculosis

complex were identified accurately at the complex level but could not be separated at the species level. All other

organisms were identified at the species level, with the exception of one strain of M. kansasii (accurately

identified but with a low spectral score) and three pairs of closely related strains: M. abscessus and M.

massiliense,M. mucogenicumandM. phocaicum, andM. chimaeraandM. intracellulare. These pairs of organisms can currently be identified only by multilocus gene sequence analysis. We conclude that MALDI-TOF MS analysis can be incorporated into the work flow of the microbiology laboratory for rapid and accurate identification of most strains of mycobacteria isolated from solid growth media.

The genus Mycobacterium consists of nearly 150 species, many of which are clinically significant. These organisms cause significant morbidity in humans, including pulmonary infec-tions, skin and soft tissue infecinfec-tions, and disseminated disease. Rapid and accurate diagnosis of mycobacterial infections is of utmost importance due to the fact that inappropriate treat-ment may lead to drug resistance or unnecessary exposure to drug toxicities. Accurate identification in the microbiology lab-oratory is challenging because biochemical testing is slow and unable to identify less common species, molecular probes are available for a limited number of species, and gene sequencing is technically cumbersome and relatively expensive.

Matrix-assisted laser desorption ionization–time of flight mass spectrometry (MALDI-TOF MS) is recognized as a pow-erful tool for the identification of bacteria and yeasts in the clinical laboratory (2, 16, 17, 18, 21). This technique allows identification of organisms on the basis of unique spectral fingerprints produced by extracted proteins (9). The method is relatively simple, rapid, and associated with significantly lower consumable costs than traditional microbiological identifica-tion methods (16). Although the MALDI-TOF MicroFlex LT mass spectrometer (Bruker Daltonics Inc., Billerica, MA) and associated software are expensive initially (approximately $200,000), the continuing consumable costs are inexpensive (less than $1 per isolate).

There has been limited work thus far on the use of MALDI-TOF MS for the identification of mycobacteria (5, 6, 10). This

paper describes our efforts to develop and validate MALDI-TOF MS for the identification of mycobacterial organisms. In this study we developed a protein extraction protocol specifi-cally designed for mycobacteria, created an identification database of clinically relevant type and reference strains of mycobacteria, and challenged the database with clinical iso-lates from our institution. We demonstrate that MALDI-TOF MS can be used in the clinical laboratory for rapid, accurate identification of mycobacteria from solid culture media.

MATERIALS AND METHODS

Mycobacterial type and reference strains and clinical isolates.The NIH

my-cobacterial database library was created from type and reference strains obtained from the American Type Culture Collection (ATCC; Manassas, VA), the Cul-ture Collection of the University of Go¨teborg (CCUG; Go¨teborg, Sweden), and the Deutsche Sammlung von Mikroorganismen (DSM; Braunschweig, Ger-many). The library was then challenged with clinical isolates recovered in the NIH Clinical Microbiology Laboratory. Clinical isolates for all mycobacterial species were obtained from patients at the NIH Clinical Center, a research hospital where studies are conducted with patients from diverse regions of the United States and worldwide, with the exception of 9Mycobacterium tuberculosis

strains that were isolated in South Korea as part of an ongoing NIH study. Identification of all clinical isolates was performed by use of the AccuProbe test (Gen-Probe, San Diego, CA) or by sequencing ofsecA1(23), 16S rRNA (4, 12), orhsp65(11) genes. The reference strains and clinical isolates were frozen at

⫺80°C until they were tested. Most strains were thawed at room temperature, subcultured onto Middlebrook 7H11 agar, and incubated at 37°C.M. marinum

was incubated at 30°C,M. xenopiwas incubated at 42°C, andM. haemophilum

was cultured onto sheep blood agar and incubated at 30°C.

Protein extraction protocol.The MALDI-TOF MS protein extraction protocol

for mycobacteria was as follows: a disposable 10-␮l inoculating loop was used to obtain mycobacterial colonies grown on Middlebrook agar. The organisms were suspended in 500␮l of distilled water in a 1.5-ml screw-cap Eppendorf tube and heated to 95°C for 30 min to kill the mycobacteria. The tube was briefly vortexed, and a plastic micropestle (pellet pestle, 749521-1500; Kimble Chase, Vineland, NJ) was subsequently used to disperse the suspension in the Eppendorf tube for approximately 30 s. The tube was centrifuged in an Eppendorf 5415D centrifuge at 13,000 rpm for 2 min, and the supernatant was completely removed. The pellet * Corresponding author. Mailing address: Microbiology Service,

De-partment of Laboratory Medicine, Clinical Center, National Institutes of Health, 10 Center Drive, MSC 1508, Bethesda, MD 20892-1508. Phone: (301) 496-4433. Fax: (301) 402-1886. E-mail: azelazny@mail .nih.gov.

Published ahead of print on 16 March 2011.

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was washed with 300␮l of distilled water and centrifuged at 13,000 rpm for 2 min, and the liquid was removed. The pellet was then suspended in 1.2 ml of 70% ethanol, vortexed briefly, and centrifuged at 13,000 rpm for 2 min. The super-natant was decanted, the pellet was briefly spun in the centrifuge, and all residual liquid was completely removed with a pipette. Fifty microliters of 70% formic acid and 100 to 200␮l of 0.1-mm-diameter glass beads (zirconia-silica beads, 36270-62; Cole-Parmer Instrument Co., Vernon Hills, IL) were added to the pellet. The suspension was vortexed for 10 min, 50␮l of 100% acetonitrile was added, and the sample was vortexed for another 10 min. The sample was cen-trifuged for 2 min at 13,000 rpm, and the supernatant was utilized for analysis by MALDI-TOF MS.

MALDI-TOF mass spectrometry.One microliter of supernatant from each

test sample was pipetted onto a spot on the MALDI-TOF steel target plate, and 1␮l of the calibration standard (protein calibration standards I and peptide calibration standards II; Bruker Daltonics Inc., Billerica, MA) was pipetted onto a separate spot. After the samples had dried, 2␮l of the MALDI matrix (a saturated solution of␣-cyano-4-hydroxycinnamic acid in 50% acetonitrile and 2.5% trifluoroacetic acid prepared daily) was pipetted onto the samples and calibration standard. A slide warmer (Premiere slide warmer, XH-2002; Daigger, Vernon Hills, IL) heated to 35°C was used to expedite uniform drying of the samples and matrix. The samples and matrix routinely dried within approxi-mately 5 min. Spectra were acquired over a mass/charge (m/z) ratio of 2,000 to 20,000 using a MALDI-TOF MicroFlex LT mass spectrometer (Bruker Dalton-ics Inc., Billerica, MA) in linear mode and summing 1,000 laser shots over 20 sites on each sample.

Spectral analysis.Criteria established by Bruker Daltonics for construction of

the reference database are that each spectrum must contain at least 25 peaks with a resolution greater than 400, of which 20 of the peaks must have a resolution greater than 500. The NIH mycobacterial database was created with spectra meeting these standards, with a minimum of 8 quality spectra per or-ganism required for entry of the mycobacterial strain into the reference database. During this study clinical isolates were run in quadruplicate, and the spectral patterns were matched with those in the NIH and the manufacturer’s databases. The BioTyper software (version 2.0.4) assigned scores of 0 to 3, with higher scores indicating a greater probability of correct organism identification. The scoring software is a proprietary algorithm, calculating a logarithmic score on the basis of spectral matching patterns. On the basis of our previous experience with bacterium and yeast identification by MALDI-TOF MS, accurate identification is obtained with scores of 1.8 or greater (17, 18).

RESULTS AND DISCUSSION

Optimization of extraction protocol for mycobacteria.

Working with mycobacteria in the open work area of the lab-oratory poses significant risks to lablab-oratory personnel. To ad-dress this, we evaluated a heat-killing protocol. Mycobacterial growth from the surface of an agar plate was collected with a disposable 10-␮l loop, transferred to a 1.5-ml Eppendorf tube with 500␮l of distilled water, and heated to 95°C for 30 min. The heated suspension was vortexed, subcultured onto Middle-brook 7H11 agar, incubated, and checked weekly for growth. The entire procedure was performed for 20 different mycobac-terial species, includingM. tuberculosis. None of the species grew after 6 weeks of incubation, indicating that the extraction protocol could be performed safely in the open laboratory after this heat-killing step.

Initial attempts at protein extraction using the protocol for bacteria and yeasts (18) did not yield adequate spectra for MALDI-TOF MS analysis. Acid-fast staining of the heated samples showed that the mycobacteria had clumped together. Different methods for dispersing the clumps were compared, including repeatedly passing the suspension through a narrow-gauge needle into a syringe, grinding the specimen in a 15-ml conical tube with a tissue grinder, and grinding the specimen in a 1.5-ml Eppendorf tube with a micropestle. Acid-fast staining demonstrated that the micropestle had dispersed the clumps more than the other techniques. In addition, the micropestle

was the least cumbersome and the most cost-effective (approx-imately $0.70 per micropestle).

Despite the successful disruption of clumps with the mi-cropestle, the quality of spectra for several species was still poor and precluded adequate organism identification. It was noted that the problematic isolates (e.g., selected strains ofM. abscessusandM. fortuitum) produced smooth colonies on solid growth media. We recognized that mycobacterial colony mor-phology may be a function of the presence of glycopeptidolip-ids (GPLs) in the cell wall, as has been shown in the case of the

M. aviumcomplex and M. smegmatis(14). We then hypothe-sized that the extraction reagents were unable to penetrate the GPL-rich cell envelope for adequate protein extraction in these isolates. Several methods for physically breaking up the cell envelopes were considered. We hypothesized that zirconia-silica beads should be able to accomplish this without destroy-ing the proteins needed for accurate identification by MALDI-TOF MS. We compared the quality of the spectra produced by beads of different diameters (0.1 mm, 0.2 mm, and 0.4 to 0.6 mm) for analysis of a smooth strain ofM. abscessus and M. fortuitum. Beads were added to the first extraction reagent (70% formic acid) in an Eppendorf tube containing one of these organisms, and the tube was vortexed for 10 min. The best results were obtained with 0.1-mm-diameter beads. After incorporation of the use of the micropestle and silica beads into the mycobacterial protein extraction protocol, we were able to generate reproducible high-quality spectra for all spe-cies of mycobacteria that were analyzed.

One issue that arose while the use of silica beads with formic acid for protein extraction was considered was the possibility that heat generated during vortexing may lead to formylation of the proteins and subsequently result in misidentification of the organisms. We addressed this concern by vortexing 10␮l of peptide standards with the beads in 70% formic acid for 10, 20, or 60 min. The negative control consisted of 1␮l of untreated peptide standards plated directly onto the MALDI-TOF steel well. For the positive control, we boiled 10␮l of the standards in 50␮l of formic acid at 55°C for 60 min prior to plating on the target. MALDI-TOF spectra were acquired and analyzed. Compared with the negative control, spectra of the positive control had shifted by multiples of 28m/z(the mass of a formyl group), indicating that formylation had occurred. No formyla-tion occurred in the samples that were vortexed for 10 or 20 min, and a minimal amount of formylation occurred in the sample that was vortexed for 60 min. Consequently, we con-cluded that no changes were needed in our 10-min extraction protocol.

Creation of mycobacterial database.Our novel protein

ex-traction protocol allowed us to create our own database of mycobacterial signatures. Forty-two type and reference strains comprising 37 species of mycobacteria were analyzed by MALDI-TOF MS and produced spectra meeting the require-ments for incorporation into the NIH mycobacterial database (Table 1). The NIH database contains three species in theM. tuberculosiscomplex (M. tuberculosis,M. bovis,M. africanum), 24 other species of slowly growing mycobacteria, and 10 spe-cies of rapidly growing mycobacteria. The Bruker database (version 3.0.2.0), on the other hand, contains 50 strains of mycobacteria, comprising 18 species. The NIH database is more comprehensive, containing additional clinically relevant

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species, includingM. bolletii,M. haemophilum,M. massiliense,

M. scrofulaceum, andM. szulgai. Similar to the Bruker data-base, our database containsM. avium; however, we were able to incorporate a more complete catalogue ofM. avium com-plex organisms that includesM. chimaera,M. colombiense,M. intracellulare, M. mantenii, and M. marseillense(Table 1). By creating our own database, we have opened the possibility for the future addition of other species of mycobacteria into the database as needs arise. This is of special importance, because the number of species within the genusMycobacteriumis in-creasing rapidly (19) and clinical laboratories will be chal-lenged to remain abreast of this ever-expanding taxonomy.

Testing the library.One hundred four clinical isolates

com-prising 17 species of mycobacteria were analyzed by the NIH mycobacteria library (Table 2). Only one isolate, anM. kansasii

strain, had a spectral score of⬍1.8. It was correctly identified but had scores ranging from 1.61 to 1.78. AllM. tuberculosis

[image:3.585.299.540.81.296.2]

complex isolates attained scores of⬎2.0 and were unambigu-ously differentiated from nontuberculous mycobacteria. An ex-ample of the spectral patterns obtained for these organisms is shown in Fig. 1. The 26 M. tuberculosis complex organisms tested included 7 isolates of multidrug-resistant (MDR) and extensively drug-resistant (XDR) Beijing and non-Beijing strains ofM. tuberculosis from patients in South Korea. The remainder of the isolates were obtained from native and for-eign-born patients referred to the NIH Clinical Center, includ-ing two strains ofM. bovis. Although MALDI-TOF MS accu-rately classified all isolates as members of M. tuberculosis

TABLE 1. Reference strains incorporated into the NIH mycobacterial MALDI-TOF database

Strain

Mycobacterium abscessusATCC 19977T Mycobacterium abscessusATCC 23040

Mycobacterium africanumATCC 25420T Mycobacterium asiaticumCCUG 29115T

Mycobacterium aviumsubsp. aviumATCC 25291T Mycobacterium bolletiiCCUG 50184T

Mycobacterium bovisATCC 19219T Mycobacterium celatumATCC 51131T Mycobacterium chelonaeATCC 35749

Mycobacterium chelonaeATCC 35751

Mycobacterium chelonaeATCC 35752T Mycobacterium chimaeraCCUG 50989T Mycobacterium colombienseDSM 45105T Mycobacterium flavescensATCC 14474T Mycobacterium fortuitumATCC 35931

Mycobacterium fortuitumATCC 6841T Mycobacterium gastriATCC 15754T Mycobacterium gordonaeATCC 14470T Mycobacterium haemophilumATCC 29548T Mycobacterium intracellulareATCC 13950T Mycobacterium kansasiiATCC 35775

Mycobacterium mageritenseCCUG 37984T Mycobacterium malmoenseATCC 29571T Mycobacterium manteniiDSM 45255T Mycobacterium marinum2006 1152a

Mycobacterium marseillenseCCUG 56325

Mycobacterium massilienseCCUG 48898T Mycobacterium mucogenicumATCC 49650T Mycobacterium nonchromogenicumATCC 19530T Mycobacterium peregrinumATCC 14467T Mycobacterium peregrinumATCC 700686

Mycobacterium phocaicumCCUG 50185T Mycobacterium scrofulaceumATCC 19981T Mycobacterium shimoideiATCC 27962T Mycobacterium simiaeATCC 25275T Mycobacterium smegmatisCCUG 21002T Mycobacterium szulgaiATCC 35799T Mycobacterium triplexATCC 700071T Mycobacterium trivialeATCC 23292T

Mycobacterium tuberculosisH37RV ATCC 27294T Mycobacterium ulceransATCC 35839

Mycobacterium xenopiATCC 19250T

aThe type strain forM. marinum,M. marinumATCC 927, was replaced by a

[image:3.585.303.539.517.696.2]

clinical isolate ofM. marinum,M. marinum2006 1152, in the database.

TABLE 2. Clinical isolates identified by MALDI-TOF MS

Species (no. of isolates tested)

No. of isolates with the following highest score:

⬍1.8 1.8–⬍1.9 1.9–⬍2.0 ⱖ2.0

M. abscessus(6)a 1 5

M. asiaticum(2) 2

M. avium(7) 1 6

M. chelonae(5) 5

M. chimaera(2)b 2

M. fortuitum(6) 6

M. gordonae(5) 5

M. intracellulare(6)b 6

M. kansasii(15) 1 3 4 7

M. marinum(5) 5

M. massiliense(6)a 1 5

M. mucogenicum(5)c 1 1 3

M. peregrinum(4) 4

M. smegmatis(1) 1

M. szulgai(2) 2

M. tuberculosiscomplex (26) 26

M. xenopi(1) 1

Total (104) 1 4 9 90

a

M. abscessusandM. massiliensewere not differentiated from each other by MALDI-TOF MS.

b

M. chimaeraandM. intracellularewere not differentiated from each other by MALDI-TOF MS.

c

M. mucogenicumwas identified asM. mucogenicumandM. phocaicumby MALDI-TOF MS.

FIG. 1. Expanded view of MALDI spectra representing 3 clinical isolates. (A) M. abscessus (BioTyper score, ⬎2.0); (B) M. kansasii

(BioTyper score,⬎1.8); (C)M. tuberculosis(BioTyper score,⬎2.0).

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complex, it was not able to separate them into the individual species. Likewise, three other pairs of closely related organ-isms could not be distinguished:M. abscessusand M. massil-iense, M. mucogenicum and M. phocaicum, and M. chimaera

andM. intracellulare.

Clinical isolates ofM. abscessusandM. massiliense, identi-fied in the microbiology laboratory by sequencing of thesecA,

rpoB, orhsp65genes, could not be discriminated from each other by MALDI-TOF. This is not surprising because mem-bers of theM. abscessusgroup (i.e.,M. abscessussensu stricto,

M. bolletii, andM. massiliense) are closely related phylogeneti-cally and cannot be differentiated readily on the basis of single-gene sequencing (7). Multilocus sequencing, as performed in our laboratory, is necessary for proper identification of these organisms (22).

MALDI-TOF MS was also unable to differentiateM. muco-genicum from M. phocaicum, another set of closely related species of rapidly growing mycobacteria (3). Similar to M. abscessusandM. massiliense, multilocus gene analysis is nec-essary for accurate differentiation of these two organisms (3).

M. mucogenicumandM. phocaicumhave similar clinical pre-sentations: both organisms usually cause catheter-related in-fections (1, 3) and have similar antibiotic susceptibility patterns (1). Thus, there are few, if any, clinical implications in the inability of MALDI-TOF MS to differentiate between these two closely related species.

The third pair of organisms that could not be differenti-ated by MALDI-TOF MS wasM. chimaeraandM. intracel-lulare. These two organisms are closely related, differing by only 1 base pair in their 16S rRNA gene regions (15, 20); however, differentiation is possible on the basis of their nucleotide differences (20 bp) in the 16S to 23S internal transcribed spacer (ITS) region. Thus, the ambiguity en-countered when these organisms are identified by MALDI-TOF MS is not surprising. Finally, there are conflicting reports as to whether or notM. chimaerais a more virulent species thanM. intracellulare(15, 20).

In our initial work developing the mycobacterial database, we experienced problems with low spectral scores when the database was challenged with theM. marinumclinical isolates. To resolve this, we replaced theM. marinumtype strain, ATCC 927, with a recent clinical isolate, M. marinum 2006 1152. When the clinical strains, as well as the original type strain, were retested all were correctly identified with spectral scores of ⬎2.0. This observation underscores the value in using a diverse collection of strains for building the database. The type strain of this species was originally described in 1926, and it is possible that significant changes in the protein profile of this species have occurred in subsequent years.

Aside from the limitations noted above, MALDI-TOF MS analysis of mycobacteria worked quite well for the identifica-tion of mycobacterial isolates in our laboratory. During the study, each clinical isolate was assayed in quadruplicate for MALDI-TOF identification so we could determine the mini-mum number of tests per sample necessary for accurate iden-tification. Of the clinical isolates with spectral scores of⬎2.0, a score of 1.8 or greater was achieved for 99% of the strains with the first spot tested. Thus, a single test is required for the identification of most organisms. Two strains of M. kansasii

had consistently low spectral scores (e.g., range, 1.7 to 1.9),

which may reflect the genetic diversity of this species. The heterogeneity ofM. kansasiihas also been encountered during analysis by sequence analysis of the 16S rRNA gene (13). Again, supplementation of the database with additional strains ofM. kansasiimay resolve this issue.

Few previous studies have addressed the utilization of MALDI-TOF MS for accurate identification of mycobacteria. Hettick et al. (6) compared the utilization of whole-cell prep-arations with protein extracts for the identification of six spe-cies ofMycobacterium. They observed that the extraction re-agents (trifluoroacetic acid and acetonitrile) but not the matrix solution inactivated mycobacteria. Since similar results were obtained with both whole cells and protein extracts, the au-thors concluded that the utilization of protein extracts is pref-erable to whole-cell preparations, as the mycobacteria are ren-dered inactive by the extraction reagents. We concur with the authors regarding the importance of using protein extracts for MALDI-TOF MS identification. Our protocol differs, how-ever, in that methods to disrupt clumps and enhance protein extraction (i.e., the utilization of the micropestle and glass beads) are incorporated into the procedure to allow accurate identification of a wide variety of mycobacteria. Furthermore, the organisms are rendered inactive at an early step in our extraction protocol by heat killing to allow all subsequent pro-cesses to be conducted in the open laboratory.

Similar to our analysis, Pignone et al. (10) were able to identify correctly a large number of mycobacteria (36 of 37 strains tested). Unlike our study, though, whole cells were used for MALDI-TOF MS analysis. We reiterate our preference in utilizing protein extracts to minimize exposure of laboratory workers to viable mycobacteria.

In a later work, Hettick et al. (5) describe their attempts to discriminate among strains of mycobacteria using MALDI-TOF MS. They conclude that strain differences are likely due to differences in relative abundance of sharedm/zvalues rather than the presence or absence of specific peaks. Although we did not attempt to discriminate among strains of the same species in our study, we do anticipate that MALDI-TOF MS can be utilized for strain differentiation of mycobacteria.

Overall, our work extends these studies by describing a spe-cific protein extraction protocol that is useful for all types of mycobacteria, as it accounts for this genus’s hardy cell enve-lope and tendency to form clumps. We also demonstrate that our extraction protocol can be utilized to create a mycobacte-rial database into which different species of mycobacteria can be incorporated indefinitely. Our results indicate that it is quite feasible to incorporate MALDI-TOF MS for routine identifi-cation of mycobacteria into the work flow of the clinical mi-crobiology laboratory. With some minor exceptions noted above, identifications were accurate to the species level. Re-sults were obtained rapidly: the turnaround time from sample preparation to results was approximately 90 min, a significant improvement when one considers the time necessary for iden-tifying mycobacteria using phenotypic tests, gene probes, or sequencing. In short, we believe that this study justifies the use of MALDI-TOF MS for the routine identification of isolated colonies ofMycobacteriumspecies. Studies of the use of this technology for identification of mycobacteria from liquid growth media are under way.

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ACKNOWLEDGMENTS

We thank Steven M. Holland for his mentorship throughout the project and his review of the manuscript. We also thank Clifton E. Barry and Isdore C. Shamputa for providing clinical strains and Yvonne R. Shea and the staff of the mycobacteriology laboratory for assisting in specimen preparation.

This research was supported by the Laboratory of Clinical Infectious Diseases and the Intramural Research Program of the NIH Clinical Center, Department of Laboratory Medicine.

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Figure

TABLE 1. Reference strains incorporated into the NIHmycobacterial MALDI-TOF database

References

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Table 1 present the results of the classical test methodology to convergence analysis of the 256 regional economies in Europe. The first column relates to the classical

First, the effects of carrier/active components mass ratio, calcination tem- perature and calcination time on catalytic activity were investigated aiming at biodiesel yield, and

תיפסכה הסנכהה תיצחמ יפל ינועה דדמ תא בשחמ ימואל חוטיבל דסומה ) וטנ ( תינויצחה 16 שפנל תינקת פל תוסנכהה

Also, Figure 4 shows that normalized error is present in a range of −6 and 3, and to estimate how this error impacts in base data, absolute frequencies were settled, from

The proposed method is to solve the total optimal fuzzy cost, fuzzy time and fuzzy quality for fuzzy multi-objective assignment problem using linear programming as follows:.. Step

difficult to estimate LOC at the beginning of a project, due to lack of information and requirements. e) Developer’s Experience: Implementation of a specific logic